Complete Test Bank With Answers
Sample Questions Posted Below
1. The decision alternative with the best expected monetary value will always be the most desirable decision.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Introduction 

2. When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaced by utility.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Introduction 

3. The outcome with the highest payoff will also have the highest utility.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

4. Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
Meaning of utility 

5. To assign utilities, consider the best and worst payoffs in the entire decision situation.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

6. A risk avoider will have a concave utility function.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

7. The expected utility is the utility of the expected monetary value.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
Expected utility approach 

8. The risk premium is never negative for a conservative decision maker.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

9. The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Expected monetary value versus expected utility 

10. The utility function for a risk avoider typically shows a diminishing marginal return for money.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

11. A game has a pure strategy solution when both players’ singlebest strategies are the same.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

12. A game has a saddle point when pure strategies are optimal for both players.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

13. A game has a saddle point when the maximin payoff value equals the minimax payoff value.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

14. The logic of game theory assumes that each player has different information.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
Introduction to game theory 

15. With a mixed strategy, the optimal solution for each player is to randomly select among two or more of the alternative strategies.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

16. The expected monetary value approach and the expected utility approach to decision making usually result in the same decision choice unless extreme payoffs are involved.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Utility and decision making 

17. A risk neutral decision maker will have a linear utility function.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

18. Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower utility value for a given outcome.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

19. Generally, the analyst must make pairwise comparisons of the decision strategies in an attempt to identify dominated strategies.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
A larger mixed strategy game 

20. When the payoffs become extreme, most decision makers are satisfied with the decision that provides the best expected monetary value.
ANSWER: 
False 
POINTS: 
1 
TOPICS: 
The meaning of utility 

21. Any 2 X 2 twoperson, zerosum, mixedstrategy game can be solved algebraically.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

22. A dominated strategy will never be selected by the player.
ANSWER: 
True 
POINTS: 
1 
TOPICS: 
Dominated strategy 

23. When consequences are measured on a scale that reflects a decision maker’s attitude toward profit, loss, and risk, payoffs are replaced by

a. 
utility values. 

b. 
multicriteria measures. 

c. 
sample information. 

d. 
opportunity loss. 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Meaning of utility 

24. The purchase of insurance and lottery tickets shows that people make decisions based on

a. 
expected value. 

b. 
sample information. 

c. 
utility. 

d. 
maximum likelihood. 
ANSWER: 
c 
POINTS: 
1 
TOPICS: 
Introduction 

25. The expected utility approach

a. 
does not require probabilities. 

b. 
leads to the same decision as the expected value approach. 

c. 
is most useful when excessively large or small payoffs are possible. 

d. 
requires a decision tree. 
ANSWER: 
c 
POINTS: 
1 
TOPICS: 
Expected utility approach 

26. Utility reflects the decision maker’s attitude toward

a. 
probability and profit 

b. 
profit, loss, and risk 

c. 
risk and regret 

d. 
probability and regret 
ANSWER: 
b 
POINTS: 
1 
TOPICS: 
Meaning of utility 

27. Values of utility

a. 
must be between 0 and 1. 

b. 
must be between 0 and 10. 

c. 
must be nonnegative. 

d. 
must increase as the payoff improves. 
ANSWER: 
d 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

28. If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be

a. 
2 to 1. 

b. 
less than 2 to 1. 

c. 
more than 2 to 1. 

d. 
unknown without further information. 
ANSWER: 
d 
POINTS: 
1 
TOPICS: 
Meaning of utility 

29. The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

a. 
the indifference probability. 

b. 
the lottery probability. 

c. 
the uncertain probability. 

d. 
the utility probability. 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

30. A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(−25000) + (1 − p)(5000). If the utility of −25,000 is 0 and of 5000 is 1, then the utility of −10,000 is
ANSWER: 
b 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

31. When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is

a. 
a risk avoider. 

b. 
a risk taker. 

c. 
an optimist. 

d. 
an optimizer. 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Risk avoiders versus risk takers 

32. A decision maker whose utility function graphs as a straight line is

a. 
conservative. 

b. 
risk neutral. 

c. 
a risk taker. 

d. 
a risk avoider. 
ANSWER: 
b 
POINTS: 
1 
TOPICS: 
Risk avoiders versus risk takers 

33. For a game with an optimal pure strategy, which of the following statements is false?

a. 
The maximin equals the minimax. 

b. 
The value of the game cannot be improved by either player changing strategies. 

c. 
A saddle point exists. 

d. 
Dominated strategies cannot exist. 
ANSWER: 
d 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

34. Which of the following statements about a dominated strategy is false?

a. 
A dominated strategy will never be selected by a player. 

b. 
A dominated strategy exists if another strategy is at least as good regardless of what the opponent does. 

c. 
A dominated strategy is superior to a mixed strategy. 

d. 
A dominated strategy can be eliminated from the game. 
ANSWER: 
c 
POINTS: 
1 
TOPICS: 
Dominated strategies 

35. A 3 x 3 twoperson zerosum game that has no optimal pure strategy and no dominated strategies

a. 
can be solved using a linear programming model. 

b. 
can be solved algebraically. 

c. 
can be solved by identifying the minimax and maximin values. 

d. 
cannot be solved. 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Larger mixed strategy games 

36. For a twoperson zerosum game, which one of the following is false?

a. 
The gain for one player is equal to the loss for the other player. 

b. 
A payoff of 2 for one player has a corresponding payoff of −2 for the other player. 

c. 
The sum of the payoffs in the payoff table is zero. 

d. 
What one player wins, the other player loses. 
ANSWER: 
c 
POINTS: 
1 
TOPICS: 
Introduction to game theory 

37. If the maximin and minimax values are not equal in a twoperson zerosum game,

a. 
a mixed strategy is optimal. 

b. 
a pure strategy is optimal. 

c. 
a dominated strategy is optimal. 

d. 
one player should use a pure strategy and the other should use a mixed strategy. 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

38. If it is optimal for both players in a twoperson, zerosum game to select one strategy and stay with that strategy regardless of what the other player does, the game

a. 
has more than one equilibrium point. 

b. 
will have alternating winners. 

c. 
will have no winner. 

d. 
has a pure strategy solution. 
ANSWER: 
d 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

39. For a twoperson, zerosum, mixedstrategy game, each player selects its strategy according to

a. 
what strategy the other player used last. 

b. 
a fixed rotation of strategies. 

c. 
a probability distribution. 

d. 
the outcome of the previous game. 
ANSWER: 
c 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

40. When the utility function for a riskneutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as

a. 
a straight line 

b. 
a convex curve 

c. 
a concave curve 

d. 
an ‘S’ curve 
ANSWER: 
a 
POINTS: 
1 
TOPICS: 
Risk avoiders versus risk takers 

41. If a game larger than 2 X 2 requires a mixed strategy, we attempt to reduce the size of the game by

a. 
identifying saddle points 

b. 
looking for dominated strategies 

c. 
inverting the payoff matrix 

d. 
eliminating negative payoffs 
ANSWER: 
b 
POINTS: 
1 
TOPICS: 
A larger mixed strategy game 

42. To select a strategy in a twoperson, zerosum game, Player A follows a ______ procedure and Player B follows a ______ procedure.

a. 
maximax, minimin 

b. 
maximax, minimax 

c. 
maximax, maximax 

d. 
maximin, minimax 
ANSWER: 
d 
POINTS: 
1 
TOPICS: 
Introduction to game theory 

43. For the payoff table below, the decision maker will use P(s_{1}) = .15, P(s_{2}) = .5, and P(s_{3}) = .35.

State of Nature 
Decision 
s_{1} 
s_{2} 
s_{3} 
d_{1} 
−5000 
1000 
10,000 
d_{2} 
−15,000 
−2000 
40,000 
a. 
What alternative would be chosen according to expected value? 
b. 
For a lottery having a payoff of 40,000 with probability p and −15,000 with probability (1 − p), the decision maker expressed the following indifference probabilities. 





Payoff 
Probability 


10,000 
.85 


1000 
.60 


−2000 
.53 


−5000 
.50 




Let U(40,000) = 10 and U(−15,000) = 0 and find the utility value for each payoff. 
c. 
What alternative would be chosen according to expected utility? 
ANSWER: 
a. 
EV(d_{1}) = 3250 and EV(d_{2}) = 10750, so choose d_{2}. 
b. 
Payoff 
Probability 
Utility 


10,000 
.85 
8.5 


1000 
.60 
6.0 


−2000 
.53 
5.3 


−5000 
.50 
5.0 



c. 
EU(d_{1}) = 6.725 and EU(d_{2}) = 6.15, so choose d_{1}. 

POINTS: 
1 
TOPICS: 
Expected utility approach 

44. A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs

State of Nature 
Decision 
s_{1} 
s_{2} 
s_{3} 
d_{1} 
5 
10 
20 
d_{2} 
−25 
0 
50 
d_{3} 
−50 
−10 
80 
Probability 
.30 
.35 
.35 
For the lottery p(80) + (1 − p)(−50), this decision maker has assessed the following indifference probabilities
Payoff 
Probability 
50 
.60 
20 
.35 
10 
.25 
5 
.22 
0 
.20 
−10 
.18 
−25 
.10 
Rank the decision alternatives on the basis of expected value and on the basis of expected utility.
ANSWER: 
EV(d_{1}) = 12 
EV(d_{2}) = 10 
EV(d_{3}) = 9.5 
EU(d_{1}) = 2.76 
EU(d_{3}) = 3.1 
EU(d_{3}) = 4.13 

POINTS: 
1 
TOPICS: 
Expected utility approach 

45. Three decision makers have assessed utilities for the problem whose payoff table appears below.

State of Nature 
Decision 
s_{1} 
s_{2} 
s_{3} 
d_{1} 
500 
100 
−400 
d_{2} 
200 
150 
100 
d_{3} 
−100 
200 
300 
Probability 
.2 
.6 
.2 

Indifference Probability for Person 
Payoff 
A 
B 
C 
300 
.95 
.68 
.45 
200 
.94 
.64 
.32 
150 
.91 
.62 
.28 
100 
.89 
.60 
.22 
−100 
.75 
.45 
.10 
a. 
Plot the utility function for each decision maker. 
b. 
Characterize each decision maker’s attitude toward risk. 
c. 
Which decision will each person prefer? 
ANSWER: 
a. 



b. 
Person A is a risk avoider, Person B is fairly risk neutral, and Person C is a risk avoider. 
c. 
For person A, EU(d_{1}) = .734 
EU(d_{2}) = .912 
EU(d_{3}) = .904 

For person B, EU(d_{1}) = .56 
EU(d_{2}) = .62 
EU(d_{3}) = .61 

For person C, EU(d_{1}) = .332 
EU(d_{2}) = .276 
EU(d_{3}) = .302 

Decision 1 would be chosen by person C. Decision 2 would be chosen by persons A and B. 

POINTS: 
1 
TOPICS: 
Risk avoiders versus risk takers 

46. A decision maker has the following utility function
Payoff 
Indifference Probability 
200 
1.00 
150 
.95 
50 
.75 
0 
.60 
−50 
0 
What is the risk premium for the payoff of 50?
ANSWER: 
EV = .75(200) + .25(−50) = 137.50
Risk premium is 137.50 − 50 = 87.50 
POINTS: 
1 
TOPICS: 
Developing utilities for monetary payoffs 

47. Determine decision strategies based on expected value and on expected utility for this decision tree. Use the utility function
Payoff 
Indifference Probability 
500 
1.00 
350 
.89 
300 
.84 
180 
.60 
100 
.43 
40 
.20 
20 
.13 
0 
0 
ANSWER: 
Let U(500) = 1 and U(0) = 0. Then
After branch 
Expected value 
Expected utility 
A 
120 
.336 
J 
316 
.680 
K 
150 
.522 
B 
127.2 
.381 
C 
100 
.430 
Based on expected value, the decision strategy is to select B. If G happens, select J. Based on expected utility, it is best to choose C. 
POINTS: 
1 
TOPICS: 
Expected utility approach 

48. Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy. The fire statistics indicate that in a given year the probability of property damage in a fire is as follows:
Fire Damage 
$100,000 
$75,000 
$50,000 
$25,000 
$10,000 
$0 
Probability 
.006 
.002 
.004 
.003 
.005 
.980 
a. 
If Burger Prince was risk neutral, how much would they be willing to pay for fire insurance? 
b. 
If Burger Prince has the utility values given below, approximately how much would they be willing to pay for fire insurance? 
Loss 
$100,000 
$75,000 
$50,000 
$25,000 
$10,000 
$5,000 
$0 
Utility 
0 
30 
60 
85 
95 
99 
100 
ANSWER: 

POINTS: 
1 
TOPICS: 
Decision making using utility 

49. Super Cola is considering the introduction of a new 8 oz. root beer. The probability that the root beer will be a success is believed to equal .6. The payoff table is as follows:

Success (s_{1}) 
Failure (s_{2}) 
Produce 
$250,000 
−$300,000 
Do Not Produce 
−$50,000 
−$20,000 
Company management has determined the following utility values:
Amount 
$250,000 
−$20,000 
−$50,000 
−$300,000 
Utility 
100 
60 
55 
0 
a. 
Is the company a risk taker, risk averse, or risk neutral? 
b. 
What is Super Cola’s optimal decision? 
ANSWER: 
a. 
Risk averse 
b. 
Produce root beer as long as p ≥ 60/105 = .571 

POINTS: 
1 
TOPICS: 
Decision making using utility 

50. Chez Paul is contemplating either opening another restaurant or expanding its existing location. The payoff table for these two decisions is:

State of Nature 
Decision 
s_{1} 
s_{2} 
s_{3} 
New Restaurant 
−$80,000 
$20,000 
$160,000 
Expand 
−$40,000 
$20,000 
$100,000 
Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and −$80,000 with probability (1−p) as follows:
Amount 
Indifference Probability (p) 
−$40,000 
.4 
$20,000 
.7 
$100,000 
.9 
a. 
Is Paul a risk avoider, a risk taker, or risk neutral? 
b. 
Suppose Paul has defined the utility of −$80,000 to be 0 and the utility of $160,000 to be 80. What would be the utility values for −$40,000, $20,000, and $100,000 based on the indifference probabilities? 
c. 
Suppose P(s_{1}) = .4, P(s_{2}) = .3, and P(s_{3}) = .3. Which decision should Paul make? Compare with the decision using the expected value approach. 
ANSWER: 
a. 
A risk avoider 
b. 
Amount 
Utility 


−$40,000 
32 


$20,000 
56 


$100,000 
72 



c. 
Decision is d_{2}; EV criterion decision would be d_{1} 

POINTS: 
1 
TOPICS: 
Decision making using utility 

51. The Dollar Department Store chain has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores and its president estimates P(s_{1}) = .4, P(s_{2}) = .3, P(s_{3}) = .1, and P(s_{4}) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000’s) and utility values below, which decision should Dollar make?
Payoff Table 
State Of The Economy 


Over The Next 5 Years 

Decision 
s_{1} 
s_{2} 
s_{3} 
s_{4} 

d_{1} — buy 10 leases 
10 
5 
0 
−20 

d_{2} — buy 5 leases 
5 
0 
−1 
−10 

d_{3} — buy 3 leases 
2 
1 
0 
−1 

d_{4} — do not buy 
0 
0 
0 
0 
Utility Table 

















Payoff (in $1,000,000’s) 
+10 
+5 
+2 
0 
−1 
−10 
−20 

Utility 
+10 
+5 
+2 
0 
−1 
−20 
−50 
ANSWER: 
Buy 3 leases. 
POINTS: 
1 
TOPICS: 
Decision making using utility 

52. Consider the following twoperson zerosum game. Assume the two players have the same two strategy options. The payoff table shows the gains for Player A.

Player B 
Player A 
Strategy b_{1} 
Strategy b_{2} 
Strategy a_{1} 
3 
9 
Strategy a_{2} 
6 
2 
Determine the optimal strategy for each player. What is the value of the game?
ANSWER: 
Mixed strategy:
Player A: .4 for a_{1}, .6 for a_{2
}Player B: .7 for b_{1}, .3 for b_{2
}
Value of game = 4.8 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

53. Consider the following twoperson zerosum game. Assume the two players have the same three strategy options. The payoff table below shows the gains for Player A.

Player B 
Player A 
Strategy b_{1} 
Strategy b_{2} 
Strategy b_{3} 
Strategy a_{1} 
3 
5 
−2 
Strategy a_{2} 
−2 
−1 
2 
Strategy a_{3} 
2 
1 
−5 
Is there an optimal pure strategy for this game? If so, what is it? If not, can the mixedstrategy probabilities be found algebraically? What is the value of the game?
ANSWER: 
There is not an optimal pure strategy.
However, there are dominated strategies.
Strategy a_{3} is dominated (by strategy a_{1}) and can be eliminated.
Then strategy b_{1} is dominated (by strategy b_{2}) and can be eliminated.
Now it is a 2 x 2 game.
Mixedstrategy probabilities are found algebraically: p = .3, (1 − p) = .7, q = .4, (1 − q) = .6
Value of game = 0.8 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

54. Suppose that there are only two vehicle dealerships (A and B) in a small city. Each dealership is considering three strategies that are designed to take sales of new vehicles from the other dealership over a period of four months. The strategies, assumed to be the same for both dealerships, are:
Strategy 1: Offer a cash rebate on a new vehicle.
Strategy 2: Offer free optional equipment on a new vehicle.
Strategy 3: Offer a 0% loan on a new vehicle.
The payoff table (in number of new vehicle sales gained per week by Dealership A (or lost by Dealership B) is shown below.

Dealership B 

Cash Rebate 
Free Options 
0% Loan 
Dealership A 
b_{1} 
b_{2} 
b_{3} 
Cash Rebate a_{1} 
2 
2 
1 
Free Options a_{2} 
−3 
3 
−1 
0% Loan a_{3} 
3 
−2 
0 
Identify the pure strategy for this twoperson zerosum game. What is the value of the game?
ANSWER: 
An optimal pure strategy exists for this game:
Dealership A should offer a cash rebate on new vehicles.
Dealership A can expect to gain a minimum of 1 new vehicle sale per week.
Dealership B should offer a 0% loan on new vehicles.
Dealership B can expect to lose a maximum of 1 new vehicle sale per week.
Value of the game is 1 new vehicle. 
POINTS: 
1 
TOPICS: 
Identifying a pure strategy 

55. Consider the following twoperson zerosum game. Assume the two players have the same two strategy options. The payoff table shows the gains for Player A.

Player B 
Player A 
Strategy b_{1} 
Strategy b_{2} 
Strategy a_{1} 
4 
8 
Strategy a_{2} 
11 
5 
Determine the optimal strategy for each player. What is the value of the game?
ANSWER: 
The optimal mixed strategy solution for this game:
Player A should select Strategy a_{1} with a .6 probability and Strategy a_{2} with a .4 probability.
Player B should select Strategy b_{1} with a .3 probability and Strategy b_{2} with a .7 probability.
Value of the game is:
Player A: 6.8 = expected gain
Player B: 6.8 = expected loss 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

56. Consider the following twoperson zerosum game. Assume the two players have the same three strategy options. The payoff table shows the gains for Player A.

Player B 
Player A 
Strategy b_{1} 
Strategy b_{2} 
Strategy b_{3} 
Strategy a_{1} 
6 
5 
−2 
Strategy a_{2} 
1 
0 
3 
Strategy a_{3} 
3 
4 
−3 
Is there an optimal pure strategy for this game? If so, what is it? If not, can the mixedstrategy probabilities be found algebraically?
ANSWER: 
There is not an optimal pure strategy. The optimal mixedstrategy probabilities can be found algebraically.
Player A should select Strategy a_{1} with a .2 probability and Strategy a_{2} with a .8 probability.
Player B should select Strategy b_{1} with a .5 probability and Strategy b_{3} with a .5 probability.
Value of the game:
For Player A: 2 = expected gain
For Player B: 2 = expected loss 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

57. Consider the following twoperson zerosum game. Assume the two players have the same three strategy options. The payoff table below shows the gains for Player A.

Player B 
Player A 
Strategy b_{1} 
Strategy b_{2} 
Strategy b_{3} 
Strategy a_{1} 
3 
2 
−4 
Strategy a_{2} 
−1 
0 
2 
Strategy a_{3} 
4 
5 
−3 
Is there an optimal pure strategy for this game? If so, what is it? If not, can the mixedstrategy probabilities be found algebraically? What is the value of the game?
ANSWER: 
There is not an optimal pure strategy. Strategy a_{1} is dominated by Strategy a_{3}, and then Strategy b_{1} is dominated by Strategy b_{2}. The optimal mixedstrategy probabilities can be found algebraically.
Player A should select Strategy a_{2} with a .8 probability and Strategy a_{3} with a .2 probability.
Player B should select Strategy b_{2} with a .5 probability and Strategy b_{3} with a .5 probability.
Value of the game = 1. 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

58. Two banks (Franklin and Lincoln) compete for customers in the growing city of Logantown. Both banks are considering opening a branch office in one of three new neighborhoods: Hillsboro, Fremont, or Oakdale. The strategies, assumed to be the same for both banks, are:
Strategy 1: Open a branch office in the Hillsboro neighborhood.
Strategy 2: Open a branch office in the Fremont neighborhood.
Strategy 3: Open a branch office in the Oakdale neighborhood.
Values in the payoff table below indicate the gain (or loss) of customers (in thousands) for Franklin Bank based on the strategies selected by the two banks.

Lincoln Bank 

Hillsboro 
Fremont 
Oakdale 
Franklin Bank 
b_{1} 
b_{2} 
b_{3} 
Hillsboro a_{1} 
4 
2 
3 
Fremont a_{2} 
6 
−2 
−3 
Oakdale a_{3} 
−1 
0 
5 
Identify the neighborhood in which each bank should locate a new branch office. What is the value of the game?
ANSWER: 
Franklin should select Hillsboro; Lincoln should select Fremont. Value of game = 2,000 customers 
POINTS: 
1 
TOPICS: 
Mixed strategy games 

59. Consider the following problem with four states of nature, three decision alternatives, and the following payoff table (in $’s):

s_{1} 
s_{2} 
s_{3} 
s_{4} 
d_{1} 
200 
2600 
1400 
200 
d_{2} 
0 
200 
– 200 
200 
d_{3} 
200 
400 
0 
200 
The indifference probabilities for three individuals are:
Payoff 
Person 1 
Person 2 
Person 3 
$ 2600 
1.00 
1.00 
1.00 
$ 400 
.40 
.45 
.55 
$ 200 
.35 
.40 
.50 
$ 0 
.30 
.35 
.45 
$ 200 
.25 
.30 
.40 
$1400 
0 
0 
0 
a. Classify each person as a risk avoider, risk taker, or risk neutral.
b. For the payoff of $400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?
c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?
ANSWER: 
a. Person 1 — risk taker; Person 2 — risk neutral; Person 3 — risk avoider
b. Risk avoider would pay $400; Risk taker would pay $200
c. Person 1 — d_{1}; Person 2 — d_{1}; Person 3 — d_{1} 
POINTS: 
1 
TOPICS: 
Risk avoiders and risk takers 

60. Metropolitan Cablevision has the choice of using one of three DVR systems. Profits are believed to be a function of customer acceptance. The payoff to Metropolitan for the three systems is:
System 
Acceptance Level 
I 
II 
III 
High 
$150,000 
$200,000 
$200,000 
Medium 
$ 80,000 
$ 20,000 
$ 80,000 
Low 
$ 20,000 
$ 50,000 
$100,000 
The probabilities of customer acceptance for each system are:
System 
Acceptance Level 
I 
II 
III 
High 
.4 
.3 
.3 
Medium 
.3 
.4 
.5 
Low 
.3 
.3 
.2 
The first vice president believes that the indifference probabilities for Metropolitan should be:
Amount 
Probability 
$150,000 
.90 
$ 80,000 
.70 
$ 20,000 
.50 
$ 50,000 
.25 
The second vice president believes Metropolitan should assign the following utility values:
Amount 
Utility 
$200,000 
125 
$150,000 
95 
$ 80,000 
55 
$ 20,000 
30 
$ 50,000 
10 
$100,000 
0 
a. Which vice president is a risk taker? Which one is risk averse?
b. Which system will each vice president recommend?
c. What system would a risk neutral vice president recommend?
ANSWER: 
a. Risk Taker — Second Vice President
Risk Avoider — First Vice President
b. First Vice President — System I
Second Vice President — System III
c. Risk Neutral Vice President — System I 
POINTS: 
1 
TOPICS: 
Risk avoiders and risk takers 

61. Consider a twoperson, zerosum game where the payoffs listed below are the winnings for Player A. Identify the pure strategy solution. What is the value of the game?

Player B Strategies 
Player A Strategies 
b_{1} 
b_{2} 
b_{3} 
a_{1} 
5 
5 
4 
a_{2} 
1 
6 
2 
a_{3} 
7 
2 
3 
ANSWER: 
Optimal pure strategies: Player A uses strategy a_{1}; Player B uses strategy b_{3}.
Value of game: Gain of 4 for Player A; loss of 4 for Player B. 
POINTS: 
1 
TOPICS: 
Game theory 

62. Consider a twoperson, zerosum game where the payoffs listed below are the winnings for Company X. Identify the pure strategy solution. What is the value of the game?

Company Y Strategies 
Company X Strategies 
y_{1} 
y_{2} 
y_{3} 
x_{1} 
3 
5 
9 
x_{2} 
8 
4 
3 
x_{3} 
7 
6 
7 
ANSWER: 
Optimal pure strategies: Company X uses strategy x_{3}; Company Y uses strategy y_{2}.
Value of game: Gain of 6 for Company X; loss of 6 for Company Y. 
POINTS: 
1 
TOPICS: 
Game theory 

63. Consider the following twoperson, zerosum game. Payoffs are the winnings for Company X. Formulate the linear program that determines the optimal mixed strategy for Company X.

Company Y Strategies 
Company X Strategies 
y_{1} 
y_{2} 
y_{3} 
x_{1} 
4 
3 
9 
x_{2} 
2 
5 
1 
x_{3} 
6 
1 
7 
ANSWER: 
Max 
GAINA 




s.t. 
4PA1 + 2PA2 + 6PA3 − GAINA ≥ 0 
(Strategy B1) 

3PA1 + 5PA2 + 1PA3 − GAINA ≥ 0 
(Strategy B2) 

9PA1 + 1PA2 + 7PA3 − GAINA ≥ 0 
(Strategy B3) 

PA1 + PA2 + PA3 = 1 
(Probabilities must sum to 1) 

PA1, PA2, PA3, GAINA ≥ 0 
(Nonnegativity) 

POINTS: 
1 
TOPICS: 
Game theory 

64. Shown below is the solution to the linear program for finding Player A’s optimal mixed strategy in a twoperson, zerosum game.
OBJECTIVE FUNCTION VALUE = 3.500 

VARIABLE 
VALUE 
REDUCED COSTS 
PA1 
0.050 
0.000 
PA2 
0.600 
0.000 
PA3 
0350 
0.000 
GAINA 
3.500 
0.000 



CONSTRAINT 
SLACK/SURPLUS 
DUAL PRICES 
1 
0.000 
−0.500 
2 
0.000 
−0.500 
3 
0.000 
0.000 
4 
0.000 
3.500 
a. 
What is Player A’s optimal mixed strategy? 
b. 
What is Player B’s optimal mixed strategy? 
c. 
What is Player A’s expected gain? 
d. 
What is Player B’s expected loss? 
ANSWER: 
a. 
Player A’s optimal mixed strategy: 
Use strategy A1 with .05 probability 


Use strategy A2 with .60 probability 


Use strategy A3 with .35 probability 



b. 
Player B’s optimal mixed strategy: 
Use strategy B1 with .50 probability 


Use strategy B2 with .50 probability 


Do not use strategy B3 



c. 
Player A’s expected gain: 3.500 




d. 
Player B’s expected loss: 3.500 


POINTS: 
1 
TOPICS: 
Game theory 

65. When and why should a utility approach be followed?
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Expected value versus utility 

66. Give two examples of situations where you have decided on a course of action that did not have the highest expected monetary value.
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Introduction 

67. Explain how utility could be used in a decision where performance is not measured by monetary value.
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Expected value versus expected utility 

68. Explain the relationship between expected utility, probability, payoff, and utility.
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Expected value versus expected utility 

69. Draw the utility curves for three types of decision makers, label carefully, and explain the concepts of increasing and decreasing marginal returns for money.
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Risk avoiders versus risk takers 

70. Game theory models extend beyond twoperson, zerosum games. Discuss two extensions (or variations).
ANSWER: 
Answer not provided. 
POINTS: 
1 
TOPICS: 
Extensions to twoperson, zerosum games 

Related
There are no reviews yet.